When would you use Simple subdivision rather than Catmull-Clark subdivision?
As an example of a case where simple is might be preferred over Catmull-Clark, say you have a large plane which you want to subdivide non-destructively for use with the displace modifier.

When subdivided with Catmull-Clark, it becomes nearly a circle:



But with Simple it maintains the original square shape:



This is just one example. There are probably many such use-cases where Catmull-Clark subdivision doesn't provide the desired result without extra things like edge-creases.